IBCapsNet: Information Bottleneck Capsule Network for Noise-Robust Representation Learning

The information bottleneck (IB) trades compression of an input $X$ against prediction of a target $Y$ through a multiplier $β=1/λ$, yet each operating point is usually served by training, or fully conditioning, a new encoder. For jointly Gaussian data, we show that the IB solution factorizes as $A(β)=D(β)W$: the information-bearing directions $W$ do not depend on $β$, and $β$ acts only through scalar gains. We ask whether this separation of representation from rate control survives beyond Gaussian models, treating the budget as a given operating parameter rather than a quantity to be optimized. For a budget-free representation $F(X)$, the separation gap is controlled by the sufficiency deficit $ε_F=I(X;Y\mid F(X))$: We show there is at least $ε_F$ in the worst case for finite inputs, and it is bounded uniformly in $λ$ by a function of $ε_F$ for finite label alphabets. The same certificate extends to a new target distribution and to pooled multi-domain data, where a conditional-alignment term appears. On MNIST, SVHN, CIFAR-10 and STL-10 (10 seeds, eight prespecified budgets), a frozen CNN representation with one compressor--decoder pair per budget reduces estimated training multiply--accumulate operations (MACs) by $7.7\times$ and wall-clock time by about $2\times$ relative to end-to-end VIBs, and attains higher budget-averaged accuracy ($65.6\%$ versus $57.3\%$ per domain; $67.1\%$ versus $57.1\%$ pooled), with the advantage concentrated at strong compression, where the VIBs collapse. At weak compression ($λ\le0.036$), VIB has higher cross-entropy and ECE; its surrogate Lagrangian is higher per domain, indistinguishable from the pooled VIB in the macro average, and lower on the pooled test set.

Spiking Neural Networks (SNNs) have shown great potential for low-power neuromorphic computing due to their event-driven processing and spatiotemporal sparsity, but they remain vulnerable to input perturbations, hardware-intrinsic noise, and adversarial attacks in real-world deployment. We attribute this vulnerability partly to input-specific hidden representations learned by standard SNNs trained with conventional cross-entropy loss, as our information-plane analysis empirically shows that substantial input-related information can still be retained after label-predictive information becomes stable. To address this issue, we propose SCIB, a simple yet effective robust learning objective for SNNs based on the Conditional Information Bottleneck. Different from conventional variational IB methods, SCIB replaces the mutual information compression term $I(X;S)$ with the conditional mutual information $I(X;S|Y)$ and derives a tractable variational upper bound. Moreover, it introduces a learnable class-conditional prior instead of a label-agnostic isotropic Gaussian prior, improving the expressiveness of variational compression and encouraging class-structured representations when combined with the supervised classification objective. Systematic experiments on Fashion-MNIST, CIFAR-10, and CIFAR-100 under external environmental noise, neuromorphic hardware noise, and adversarial attacks show that SCIB improves robustness over standard SNNs and IB-based baselines under most evaluated noise conditions, improves adversarial accuracy under the evaluated attacks without using adversarial training, and reduces the SynOps-based single-sample inference energy consumption by 24.9% relative to an unconstrained SNN baseline.

Concept Bottleneck Models (CBMs) aim to deliver interpretable predictions by routing decisions through a human-understandable concept layer, yet they often suffer reduced accuracy and concept leakage that undermines faithfulness. We introduce an explicit Information Bottleneck regularizer on the concept layer that penalizes $I(X;C)$ while preserving task-relevant information in $I(C;Y)$, encouraging minimal-sufficient concept representations. We derive two practical variants (a variational objective and an entropy-based surrogate) and integrate them into standard CBM training without architectural changes or additional supervision. Evaluated across six CBM families and three benchmarks, the IB-regularized models consistently outperform their vanilla counterparts. Information-plane analyses further corroborate the intended behavior. These results indicate that enforcing a minimal-sufficient concept bottleneck improves both predictive performance and the reliability of concept-level interventions. The proposed regularizer offers a theoretic-grounded, architecture-agnostic path to more faithful and intervenable CBMs, resolving prior evaluation inconsistencies by aligning training protocols and demonstrating robust gains across model families and datasets.